Ursula K. Le Guin, in Amazing Stories , Sept. 1992, published
"The Rock That Changed Things" (pp. 9-13) and her story from
thirty years earlier, "April in Paris" (Fantastic Stories , Sept. 1962.)
The latter (pp. 14-19) was followed by some brief remarks (p. 19)
comparing the two stories.

… And at this point a wise, old nur, so excellent at maintaining patterns that the obls let him live even after he was maimed, enters the discussion to do some pattern criticism. For a first-order approximation reading, he suggests "It might say, 'The nur places stones,'" and others fill in that the nur would be Bu. Ko corrects them with "patterns aren't ever about nurs!" and Bu counters with "Maybe patterns made of colors are." Looking with all three of his eyes, Ko reads, "—'the nur places stones beautifully in uncontrollable loopingness …. foreshadowing the seen.'" Un suggests "The vision" but cannot figure out the last word. Bu is very excited, inferring that "the patterns of the colors …. aren't accidental. Not meaningless. All the time, we have been putting them here in patterns—not just ones the obls design and we execute, but other patterns—nur patterns—with new meanings." Amid the straight lines of the obls' designs they now see, "other designs, less complete, often merely sketched or hinted—circles, spirals, ovals, and complex curvilinear mazes and labyrinths of great and unpredictable beauty and significance. *** Both patterns were there; did one cancel the other, or was each part of the other? It was difficult to see them both at once, but not impossible." Had the nurs done this all totally unconsciously "without even knowing we were doing it?" Un admits to having looked at colors, and so did Ko, plus "grain and texture." Un warns them to keep word of their works from the Professors: "They don't like patterns to change…. It makes them nervous"— and nervous Professors are dangerous to nurs (62-63).

Bu, however "was so excited and persuasive" about colors of stones "that other nurs of Obling began studying the color patterns, learning how to read their meanings." And the practice spreads. Soon, all sorts of nurs were finding "wild designs in colored stones, and surprising messages concerning obls, nurs, and blits" (64) Conservative nurs— "Many nurs," we're told—resist the trend. "If we start inventing new meanings, changing things, disturbing the patterns, where will it end?" It is unclear just how many of the nurs believe «Mr. Charlie treats us real good»—or, as we soon see, Ms. Charlie—but certainly not Bu; she "would hear none of that; she was full of her discovery. She no longer listened in silence. She spoke." Bu goes up to the Rectory Mosaic, wearing around her neck a turquoise that she calls her "selfstone." Up at the Mosaic, Bu crouches before the Rectoress and asks "Would the Lady Rectoress in her kindness answer a question I have?"

Friday, August 1, 2014

In related news at the website of the
American Mathematical Society today:

Multimillion-Dollar Minds

“The Multimillion-Dollar Minds of 5 Mathematical Masters,”by Kenneth Chang, ran in the New York Times on June 23, 2014.
The piece reports the award of $3 million “Breakthrough” prizes….
The prizes are financed by Yuri Milner, “a Russian who dropped out
of graduate studies in physics and became a successful investor in
Internet companies like Facebook,” and Mark Zuckerberg,
the founder of Facebook….

Saturday, May 11, 2013

Book Description
"Publication Date: April 23, 2013
James Blish called him the “finest conscious artist
science fiction ever produced.” Kurt Vonnegut based
the famous character Kilgore Trout on him. And
such luminaries as Harlan Ellison, Stephen King, and
Octavia Butler have hailed him as a mentor.
Theodore Sturgeon was both a popular favorite and
a writer’s writer…."

SOCRATES: Is he not better off in knowing his ignorance?
MENO: I think that he is.
SOCRATES: If we have made him doubt, and given him the 'torpedo's shock,' have we done him any harm?
MENO: I think not.

Sunday, October 21, 2012

"The fundamental unity of the Sequency and Simultaneity
points of view became plain; the concept of interval served
to connect the static and the dynamic aspect of the universe.
How could he have stared at reality for ten years and not
seen it? There would be no trouble at all in going on.
Indeed he had already gone on. He was there."

Tuesday, March 27, 2012

There was silence then: deep silence. We both gazed, I afoot, Rover kneeling, at the box. No sound. Nothing happened. Nothing would happen. Nothing would ever happen, until we lifted the lid of the box.

“Like Pandora,” I said in a weak whisper. I could not quite recall Pandora’s legend. She had let all the plagues and evils out of the box, of course, but there had been something else, too. After all the devils were let loose, something quite different, quite unexpected, had been left. What had it been? Hope? A dead cat? I could not remember.

Impatience welled up in me. I turned on Rover, glaring. He returned the look with expressive brown eyes. You can’t tell me dogs haven’t got souls.

“Just exactly what are you trying to prove?” I demanded.

“That the cat will be dead, or not dead,” he murmured submissively. “Certainty. All I want is certainty. To know for sure that God does play dice with the world.”

I looked at him for a while with fascinated incredulity. “Whether he does, or doesn’t,” I said, “do you think he’s going to leave you a note in the box?” I went to the box, and with a rather dramatic gesture, flung the lid back. Rover staggered up from his knees, gasping, to look. The cat was, of course, not there.

“We used to think so,” I said, “but really we should use larger boxes.”

He gazed about in mute bewilderment, and did not flinch even when the roof of the house was lifted off just like the lid of the box, letting in the unconscionable, inordinate light of the stars. He had just time to breathe, “Oh, wow!”

I have identified the note that keeps sounding. I checked it on the mandolin before the glue melted. It is the note A, the one that drove the composer Schumann mad. It is a beautiful, clear tone, much clearer now that the stars are visible. I shall miss the cat. I wonder if he found what it was we lost?

Friday, October 21, 2011

The above image illustrates an equivalence* between sequential and simultaneous points of view.

The sequential point of view says "Do," the simultaneous point of view says "Be."

And then there is the Sinatra point of view—

"The fundamental unity of the Sequency and Simultaneity points of view became plain; the concept of interval served to connect the static and the dynamic aspect of the universe. How could he have stared at reality for ten years and not seen it? There would be no trouble at all in going on. Indeed he had already gone on. He was there."

“The purer, the more euclidean the reason that builds a utopia, the greater is its self-destructive capacity. I submit that our lack of faith in the benevolence of reason as the controlling power is well founded. We must test and trust our reason, but to have faith in it is to elevate it to godhead.”

“Utopia has been euclidean, it has been European, and it has been masculine. I am trying to suggest, in an evasive, distrustful, untrustworthy fashion, and as obscurely as I can, that our final loss of faith in that radiant sandcastle may enable our eyes to adjust to a dimmer light and in it perceive another kind of utopia.”

“You will recall that the quality of static perfection is an essential element of the non-inhabitability of the euclidean utopia….”

“The euclidean utopia is mapped; it is geometrically organized, with the parts labeled….”

— Ursula K. Le Guin, “A Non-Euclidean View of California as a Cold Place to Be”

"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."

Monday, April 26, 2010

“There was a wall. It did not look important. It was built of uncut rocks roughly mortared. An adult could look right over it, and even a child could climb it. Where it crossed the roadway, instead of having a gate it degenerated into mere geometry, a line, an idea of boundary. But the idea was real. It was important. For seven generations there had been nothing in the world more important than that wall.

Like all walls it was ambiguous, two-faced. What was inside it and what was outside it depended upon which side of it you were on.”

Note—

“We note that the phrase ‘instead of having a gate it degenerated into mere geometry’ is mere fatuousness. If there is an idea here, degenerate, mere, and geometry in concert do not fix it. They bat at it like a kitten at a piece of loose thread.”

(For the phrase mere geometry elsewhere, see a note of April 22. The apparently flat figures in that note’s illustration “Galois Affine Geometry” may be regarded as degenerate views of cubes.)

Later in the Le Guin novel—

“… The Terrans had been intellectual imperialists, jealous wall builders. Even Ainsetain, the originator of the theory, had felt compelled to give warning that his physics embraced no mode but the physical and should not be taken as implying the metaphysical, the philosophical, or the ethical. Which, of course, was superficially true; and yet he had used number, the bridge between the rational and the perceived, between psyche and matter, ‘Number the Indisputable,’ as the ancient founders of the Noble Science had called it. To employ mathematics in this sense was to employ the mode that preceded and led to all other modes. Ainsetain had known that; with endearing caution he had admitted that he believed his physics did, indeed, describe reality.

Strangeness and familiarity: in every movement of the Terran’s thought Shevek caught this combination, was constantly intrigued. And sympathetic: for Ainsetain, too, had been after a unifying field theory. Having explained the force of gravity as a function of the geometry of spacetime, he had sought to extend the synthesis to include electromagnetic forces. He had not succeeded. Even during his lifetime, and for many decades after his death, the physicists of his own world had turned away from his effort and its failure, pursuing the magnificent incoherences of quantum theory with its high technological yields, at last concentrating on the technological mode so exclusively as to arrive at a dead end, a catastrophic failure of imagination. Yet their original intuition had been sound: at the point where they had been, progress had lain in the indeterminacy which old Ainsetain had refused to accept. And his refusal had been equally correct– in the long run. Only he had lacked the tools to prove it– the Saeba variables and the theories of infinite velocity and complex cause. His unified field existed, in Cetian physics, but it existed on terms which he might not have been willing to accept; for the velocity of light as a limiting factor had been essential to his great theories. Both his Theories of Relativity were as beautiful, as valid, and as useful as ever after these centuries, and yet both depended upon a hypothesis that could not be proved true and that could be and had been proved, in certain circumstances, false.

But was not a theory of which all the elements were provably true a simple tautology? In the region of the unprovable, or even the disprovable, lay the only chance for breaking out of the circle and going ahead.

In which case, did the unprovability of the hypothesis of real coexistence– the problem which Shevek had been pounding his head against desperately for these last three days. and indeed these last ten years– really matter?

He had been groping and grabbing after certainty, as if it were something he could possess. He had been demanding a security, a guarantee, which is not granted, and which, if granted, would become a prison. By simply assuming the validity of real coexistence he was left free to use the lovely geometries of relativity; and then it would be possible to go ahead. The next step was perfectly clear. The coexistence of succession could be handled by a Saeban transformation series; thus approached, successivity and presence offered no antithesis at all. The fundamental unity of the Sequency and Simultaneity points of view became plain; the concept of interval served to connect the static and the dynamic aspect of the universe. How could he have stared at reality for ten years and not seen it? There would be no trouble at all in going on. Indeed he had already gone on. He was there. He saw all that was to come in this first, seemingly casual glimpse of the method, given him by his understanding of a failure in the distant past. The wall was down. The vision was both clear and whole. What he saw was simple, simpler than anything else. It was simplicity: and contained in it all complexity, all promise. It was revelation. It was the way clear, the way home, the light.”

“In a letter to Harriet Monroe, written December 23, 1926, Stevens refers to the Sapphic fragment that invokes the genius of evening: ‘Evening star that bringest back all that lightsome Dawn hath scattered afar, thou bringest the sheep, thou bringest the goat, thou bringest the child home to the mother.’ Christmas, writes Stevens, ‘is like Sappho’s evening: it brings us all home to the fold’ (Letters of Wallace Stevens, 248).”

— “The Archangel of Evening,” Chapter 5 of Wallace Stevens: The Intensest Rendezvous, by Barbara M. Fisher, The University Press of Virginia, 1990

Comments Off on Types of Ambiguity

Thursday, April 22, 2010

“Mereology (from the Greek μερος, ‘part’) is the theory of parthood relations: of the relations of part to whole and the relations of part to part within a whole. Its roots can be traced back to the early days of philosophy, beginning with the Presocratics….”

A non-Euclidean* approach to parts–

Corresponding non-Euclidean*projective points —

Richard J. Trudeau in The Non-Euclidean Revolution, chapter on “Geometry and the Diamond Theory of Truth”–

“… Plato and Kant, and most of the philosophers and scientists in the 2200-year interval between them, did share the following general presumptions:

“Then, on impulse, Phædrus went over to his bookshelf and picked out a small, blue, cardboard-bound book. He’d hand-copied this book and bound it himself years before, when he couldn’t find a copy for sale anywhere. It was the 2,400-year-old Tao Te Ching of Lao Tzu. He began to read….

Phædrus read on through line after line, verse after verse of this, watched them match, fit, slip into place. Exactly. This was what he meant. This was what he’d been saying all along, only poorly, mechanistically. There was nothing vague or inexact about this book. It was as precise and definite as it could be. It was what he had been saying, only in a different language with different roots and origins. He was from another valley seeing what was in this valley, not now as a story told by strangers but as a part of the valley he was from. He was seeing it all.

He had broken the code.

He read on. Line after line. Page after page. Not a discrepancy. What he had been talking about all the time as Quality was here the Tao, the great central generating force of all religions, Oriental and Occidental, past and present, all knowledge, everything.”

Monday, October 21, 2002

The entry below, "Theology for a Small Planet," sketches an issue that society has failed to address since the fall of 1989, when it was first raised by the Harvard Divinity Bulletin.

In honor mainly of Ursula K. Le Guin, but also of her fellow authors above, I offer Le Guin's solution. It is not new. It has been ignored mainly because of the sort of hateful and contemptible arrogance shown by

executives in the tradition of Henry Ford and later Ford Foundation and Ford Motors employees McGeorge Bundy and Robert McNamara (see yesterday's entry below for Ford himself), by

theologians in the tradition of the Semitic religions — Judaism, Christianity, and Islam — and by

self-proclaimed "shamans of scientism" like Michael Shermer in the tradition of Scientific American magazine.

Here is an introduction to the theology that should replace the ridiculous and outdated Semitic religions.

"Scholarly translators of the Tao Te Ching, as a manual for rulers, use a vocabulary that emphasizes the uniqueness of the Taoist 'sage,' his masculinity, his authority. This language is perpetuated, and degraded, in most popular versions. I wanted a Book of the Way accessible to a present-day, unwise, unpowerful, and perhaps unmale reader, not seeking esoteric secrets, but listening for a voice that speaks to the soul. I would like that reader to see why people have loved the book for 2500 years.

It is the most lovable of all the great religious texts, funny, keen, kind, modest, indestructibly outrageous and inexhaustibly refreshing. Of all the deep springs, this is the purest water. To me it is also the deepest spring."

Tuesday, September 24, 2002

When you stand in the dark and look at a star a hundred light years away, not only have the retarded light waves from the star been travelling for a hundred years toward your eyes, but also advanced waves from your eyes have reached a hundred years into the past to encourage the star to shine in your direction.

He’d toyed with “psi” himself…. The reason he and so many other theoretical physicists were suckers for the stuff was easy to understand — for two-thirds of a century an enigma had rested at the heart of theoretical physics, a contradiction, a hard kernel of paradox….

Peter [Slater] had never thirsted after “hidden variables” to explain what could not be pictured. Mathematical relationships were enough to satisfy him, mere formal relationships which existed at all times, everywhere, at once. It was a thin nectar, but he was convinced it was the nectar of the gods.

………………

Those so-called crazy psychics were too sane, that was their problem — they were too stubborn to admit that the universe was already more bizarre than anything they could imagine in their wildest dreams of wizardry. (Ch. 16)

Minakis caught up and walked beside him in silence, moving with easy strides over the bare ground, listening as Peter [Slater] spoke. “Delos One was ten years ago — quantum theory seemed as natural as water to me then; I could play in it without a care. If I’d had any sense of history, I would have recognized that I’d swallowed the Copenhagen interpretation whole.”

“Back then, you insisted that the quantum world is not a world at all,” Minakis prompted him. “No microworld, only mathematical descriptions.”

“Yes, I was adamant. Those who protested were naive — one has to be willing to tolerate ambiguity, even to be crazy.”

“Bohr’s words?”

“The party line. Of course Bohr did say, ‘It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.’ Meaning that when we start to talk what sounds like philosophy, our colleagues should rip us to pieces.” Peter smiled. “They smell my blood already.”

………………

Peter glanced at Minakis. “Let’s say there are indications — I have personal indications — not convincing, perhaps, but suggestive, that the quantum world penetrates the classical world deeply.” He was silent for a moment, then waved his hand at the ruins. “The world of classical physics, I mean. I suppose I’ve come to realize that the world is more than a laboratory.”

“We are standing where Apollo was born,” Minakis said. “Leto squatted just there, holding fast to a palm tree, and after nine days of labor gave birth to the god of light and music….”

To Lucero, in memory of 1962 in Cuernavaca

From On Beauty, by Elaine Scarry, Princeton University Press, 1999 —

“Homer sings of the beauty of particular things. Odysseus, washed up on shore, covered with brine, having nearly drowned, comes upon a human community and one person in particular, Nausicaa, whose beauty simply astonishes him. He has never anywhere seen a face so lovely; he has never anywhere seen any thing so lovely….

I have never laid eyes on anyone like you, neither man nor woman… I look at you and a sense of wonder takes me.

Wait, once I saw the like — in Delos, beside Apollo’s altar — the young slip of a palm-tree springing into the light.”

“When we try to look inside atoms,” Peter said, “not only can we not see what’s going on, we cannot even construct a coherent picture of what’s going on.”

“If you will forgive me, Peter,” Minakis said, turning to the others. “He means that we can construct several pictures — that light and matter are waves, for example, or that light and matter are particles — but that all these pictures are inadequate. What’s left to us is the bare mathematics of quantum theory.”

…. “Whatever the really real world is like, my friend, it is not what you might imagine.”

………………

Talking physics, Peter tended to bluntness. “Tell me more about this real world you imagine but can’t describe.”

Minakis turned away from the view of the sunset. “Are you familiar with John Cramer’s transactional interpretation of quantum mechanics?”

Sunday, September 15, 2002

An article in the current New York Review of Books (dated Sept. 26) on Ursula K. Le Guin prompted me to search the Web this evening for information on a short story of hers I remembered liking. I found the following in the journal of mathematician Peter Berman:

A Fisherman of the Inland Sea, Ursula K. Le Guin, 1994:A book of short stories. Good, entertaining. I especially liked “The Rock That Changed Things.” This story is set in a highly stratified society, one split between elite and enslaved populations. In this community, the most important art form is a type of mosaic made from rocks, whose patterns are read and interpreted by scholars from the elite group. The main character is a slave woman who discovers new patterns in the mosaics. The story is slightly over-the-top but elegant all the same.

I agree that the story is elegant (from a mathematician, a high compliment), so searched Berman’s pages further, finding this:

between The French Mathematician (a novel about Galois) and Harry Potter and the Sorcerer’s Stone.

My own version of the Philosopher’s Stone (the phrase used instead of “Sorcerer’s Stone” in the British editions of Harry Potter) appears in my profile picture at top left; see also the picture of Plato’s diamond figure in my main math website. The mathematics of finite (or “Galois”) fields plays a role in the underlying theory of this figure’s hidden symmetries. Since the perception of color plays a large role in the Le Guin story and since my version of Plato’s diamond is obtained by coloring Plato’s version, this particular “rock that changes things” might, I hope, inspire Berman to extend his table to include Le Guin’s tale as well.

Even the mosaic theme is appropriate, this being the holiest of the Mosaic holy days.